The law, backed by the government of President Cristina Kirchner, was adopted in a 33-27 vote after 15 hours of debate.
Ruling party leader Miguel Pichetto said: 'It is a historic day.'
Opposition senator Gerardo Morales said Argentine society has changed, stressing that the bill was aimed at guaranteeing the rights of minorities.
The law changes the legal code, which will no longer refer to husband and wife, but rather to 'the marrying parties'.
Same-sex couples will have the same rights as heterosexuals in terms of adoptions, social security and family time.
Argentina is the first country in Latin America to give a green light to same-sex marriage nationwide.
It follows the Netherlands, Belgium, Spain, Canada, South Africa, Norway, Sweden, Portugal and Iceland.
